When did God stop dealing with the Gentiles and start dealing with the Jews only?

God stopped dealing with the Gentiles and began dealing with the Jews only at the call of Abraham, around 2000 B.C. From that point until the New Testament, God primarily dealt with the nation of Israel, though there were exceptions such as Nineveh.

Les explains that after the confusion of languages and another 175 to 200 years, the whole new generation was steeped in idolatry, even Terah, Abraham's father, served other gods. So God said He had to do something different. He called out Abraham from Ur of the Chaldees, and at that point God left off dealing with the Gentiles and began dealing with Jew only, but with exceptions. The primary Old Testament exception was Nineveh, where God sent Jonah to a Gentile city. From 2000 B.C. up into the New Testament, it was primarily God dealing with the nation of Israel, Jew only, based on the promises made to Abraham. Then John the Baptist and Christ appeared to fulfill those promises, but that generation of Israelites rejected, killed, and crucified Him.

Genesis 12:1

Now the LORD had said unto Abram, Get thee out of thy country, and from thy kindred, and from thy father’s house, unto a land that I will shew thee:

What does God do with the Gentile nations from Genesis 12 onward?

From Genesis 12 onward, God allows the Gentile nations to continue on like a mass river, while He pulls Abram out to become the nation of Israel. God then deals peculiarly with Israel, Jew only with exceptions, such as sending Jonah to the Gentile city of Nineveh.